Dynamic coloring of graphs having no K5 minor

被引：8
|
作者：
Kim, Younjin [1 ]
Lee, Sang June [2 ]
Oum, Sang-il [3 ,4 ]
机构：
[1] Ewha Womans Univ, Dept Math, Seoul, South Korea
[2] Duksung Womens Univ, Dept Math, Seoul, South Korea
[3] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon, South Korea
[4] KIAS, Sch Math, Seoul, South Korea
来源：
DISCRETE APPLIED MATHEMATICS | 2016年 / 206卷
基金：
新加坡国家研究基金会;
关键词：
Dynamic coloring; Minor-free graph; Four color theorem; Hadwiger's conjecture; LOCAL CHROMATIC NUMBER; CONJECTURE;
D O I：
10.1016/j.dam.2016.01.022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that every simple connected graph with no K5 minor admits a proper 4-coloring such that the neighborhood of each vertex v having more than one neighbor is not monochromatic, unless the graph is isomorphic to the cycle of length 5. This generalizes the result on planar graphs by 5.-J. Kim, W.J. Park and the second author [Discrete Appl. Math. 161 (2013) 2207-22121. (C) 2016 Elsevier B.V. All rights reserved.
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页码：81 / 89
页数：9
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